Instructions for Use
A P.I. R2 Mini-Mystery
Students will calculate each solution using
the quadratic formula. Then they will look
at the key on the right of the page to find
their answer. Be careful: there are incorrect
answers mixed in with the correct ones!
Students will write the letter that is
associated with their correct answer in the
coded message at the bottom of the page.
Solving the Case
When they have finished all 15 questions and
filled in all the blanks, students will learn the
clue that was found in the briefcase.
Backstory
Ray Radicand is a Private Investigator and owner of an agency he calls R2 P.I. The Case of Ms.
Mann’s Briefcase is the third part of a larger case. In the first activity (Solving Quadratics by
Factoring) Ray and his assistants discovered that Ms. Mann had murdered Mr. Quad.
During the search of her home following this discovering, Ray and his team found Ms. Mann’s locked
briefcase. Fortunately he also found some clues to the combination. In this second activity, students
solve quadratic equations by completing the square and then solve a logic puzzle to unlock the
briefcase.
Now it’s up to your students to help him decipher the message that he’s found. This clue surely will
lead our trusty sleuth to the place Ms. Mann is hiding.
Make sure to follow
Ready-Made Resources
so you don’t miss any
upcoming mysteries!
Who Killed Mr. Quad:
Solving Quadratics
by Factoring
The Case of Ms. Mann’s
Briefcase:
Solving Quadratics by
Completing the Square
NAME
DATE
PERIOD
A P. I . R 2 Mini-Mystery
The Message in the Briefcase
Directions: Calculate each answer below, then use your solutions to discover what Ray Radicand
found in Ms. Mann’s briefcase.
1.
3.
5.
7.
9.
4
9
+ 11 − 20 = 0
+ 2 = 11
6
4.
3
− 7 − 14 = 0
6.
6
+ 11 = −3
8.
5
5
2.
− 2 − 10 = 0
= 2 +3
− 9 = −14
A
1 ± √51
5
1 ± √3
2
C
4 ± √30
D
1
{− , 1}
3
−4 ± √46
−3
3
{− , 1}
5
7 ± √97
12
5
{−4, }
4
9 ± √193
−4
1
{− , 1}
4
−5 ± √5
2
7 ± √97
12
−7 ± √−83
6
5
−1,
4
1 2
{ , }
2 3
4
{1, − }
3
2 1
{ ,− }
3 2
3 1
{− , − }
2 3
E
F
= − +1
10. 3
Answer
B
− 7 = −2
−2
Code
Letter
G
H
−2 = −
I
J
11.
+ 8 = −10
−3
12. 4
−
= 5
K
L
13.
= 8 + 14
14. 7
− 3 = 10
M
N
15. −4 = −3
−
O
P
What did Ray Radicand find in Ms. Mann’s briefcase?
Q
R
9
7
11
13
11
6
15
10
2
4
7
4
12
11
3
9
8
10
7
6
.
10
4
−2 ± √2
T
2
{−1, }
3
10
{−1, }
7
11
{− , 1}
9
U
9
S
5
14
7
6
13
1
15
W
X
{−4, 2}
Y
−1 ± √5
2
7 ± √217
6
Z
NAME
DATE
PERIOD
A P. I . R 2 Mini-Mystery
The Message in the Briefcase
Directions: Calculate each answer below, then use your solutions to discover what Ray Radicand
found in Ms. Mann’s briefcase.
1.
3.
5.
7.
9.
11.
13.
4
9
3
6
5
−3
+ 11 − 20 = 0
2.
+ 2 = 11
4.
− 7 − 14 = 0
+ 11
6.
= −3
6
12. 4
= 8 + 14
− 7 = −2
− 9 = −14
= − +1
10. 3
+ 8 = −10
= 2 +3
−2
8.
− 2 − 10 = 0
15. −4 = −3
5
14. 7
−2 = −
−
= 5
− 3 = 10
−
What did Ray Radicand find in Ms. Mann’s briefcase?
9
7
11
13
11
6
15
10
2
4
7
9
4
12
11
3
9
8
10
7
6
.
10
4
5
14
7
6
13
1
15
Code
Letter
Answer
A
{-1.2283, 1.6283}
B
{-0.3660, 2.7321}
C
{-1.4772, 9.4772}
D
{-0.3333, 1}
E
{-0.9274, 3.5941}
F
{-0.6, 1}
G
{-0.2374, 1.4041}
H
{-4, 1.25}
I
{-5.7231, 1.2231}
J
{-0.25, 1}
K
{-3.6180, -1.3820}
L
{-0.2374, 1.4041}
M
{-8.5184, -5.4816}
N
{-1, 1.25}
O
{0.5, 0.6667}
P
{-1.3333, 1}
Q
{-0.5, 0.6667}
R
{-0.3333, 1.5}
S
{-3.4142, -0.5858}
T
{-1, 0.6667}
U
{-1, 1.4286}
W
{-1.2222, 1}
X
{−4, 2}
Y
{-1.6180, 0.6180}
Z
{-1.2885, 3.6218}
NAME
DATE
PERIOD
A P. I . R 2 Mini-Mystery
The Message in the Briefcase
Directions: Calculate each answer below, then use your solutions to discover what Ray Radicand
found in Ms. Mann’s briefcase.
1.
4
+ 11 − 20 = 0
9
5.
7.
3
6
4.
− 7 − 14 = 0
±√
11.
13.
15.
5
6.
Z
R
−3 + 8 = −10
− ±√
−
= 8 + 14
±√
−4 = −3
−
10.
A
3
O
E
4
C
− 3 = 10
{
,− }
U
P T
F O R
9
7
6
15
2
9
10
O N E -W A Y
4
12
11
3
L
M
N
9
8
−2 ± √2
T
2
{−1, }
3
10
{−1, }
7
11
{− , 1}
9
I
P
U
10
6
15
W
7
10
5
13
6
S
T R
C H.
7
R
7
Z U R I
14
Q
4
T O
4
K
P
I
A
H
O
R E C E
11
1
{− , 1}
3
−4 ± √46
−3
3
{− , 1}
5
7 ± √97
12
5
{−4, }
4
9 ± √193
−4
1
{− , 1}
4
−5 ± √5
2
7 ± √97
12
−7 ± √−83
6
5
−1,
4
1 2
{ , }
2 3
4
{1, − }
3
2 1
{ ,− }
3 2
3 1
{− , − }
2 3
J
A
13
D
I
What did Ray Radicand find in Ms. Mann’s briefcase?
11
4 ± √30
G
P
{− , }
C
Y
N
7
1 ± √51
5
1 ± √3
2
F
T
{ ,− }
14.
A
E
= 5
−
Answer
I
−2 = −
{ ,− }
12.
Code
Letter
B
− 7 = −2
−2 − 9 = −14
±√
−
=− +1
− ±√
8.
− 2 − 10 = 0
±√
F
{ , }
+ 11 = −3
{− , − }
9.
6
W
, }
= 2 +3
{− , }
+ 2 = 11
{−
5
H
{− , }
3.
2.
1
X
{−4, 2}
Y
−1 ± √5
2
7 ± √217
6
Z